University of Warwick 2008/09
Department of Chemistry CH162 Workshop
CH162 Intro to Physical Chemistry
Chemical Kinetics: Workshop
Question 2:
When benzophenone is illuminated with ultraviolet light, it is excited into a singlet
state. Triethylamine acts as a quencher for the singlet state. In a time-resolved laser
spectroscopy experiment, the emission lifetime of this excited state varied with amine
concentration as shown below:
Experiment [Q] (mol dm-3) τ (s)
I 1x10-3 2.5x10-5
II 5x10-3 1.7x10-5
III 1x10-2 1.2x10-5
Determine, either graphically or by inspection, both the quenching rate constant and
fluorescence lifetime.
1
University of Warwick 2008/09
Department of Chemistry CH162 Workshop
Model answer
Question 2:
Note: You are expected to know how to derive the Stern-Volmer equation by using
the steady state approximation to obtain expressions for both fluorescence quantum
yields with/without quencher and then manipulating these equations. See lecture notes
for details. This question tests you ability to establish which equation to use to tackle
this problem and how to use it.
The Stern-Volmer equation relating to lifetimes should be used for this problem. The
Stern-Volmer equation is given by:
1 1
k Q [Q] (of a similar form as y = c + mx, where c is the intercept (1/T0)
T T0
and m is the gradient (kQ))
where T is the measured emission lifetime of the excited state, T0 is the emission
lifetime in the absence of quencher, kQ is the quenching rate constant and [Q] is the
concentration of quencher.
Graphical solution:
By plotting 1/T versus [Q] both the quenching rate constant (5.0x106 dm3 mol-1 s-1)
and fluorescence lifetime (28.6 μs) may be inferred. The quenching rate constant is
the gradient and the fluorescence lifetime is 1/intercept.
[Q]/moldm^-3 T/s 1/T / s^-1
0.001 2.50E-05 4.00E+04
0.005 1.70E-05 5.88E+04
0.01 1.20E-05 8.33E+04
1.0E+05
y = 5E+06x + 35021
R2 = 0.9999
7.5E+04
1/T /(s^-1)
5.0E+04
2.5E+04
0.0E+00
-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012
[Q]/moldm^-3
2
University of Warwick 2008/09
Department of Chemistry CH162 Workshop
Solution by inspection:
As this is a linear plot with all points lying on the line, we can calculate the quenching
rate constant and fluorescence lifetime.
y 2 y1
The gradient of a straight line is given by:
x 2 x1
From the table;
[Q]/moldm^-3 T/s 1/T / s^-1
0.001 2.50E-05 4.00E+04
0.005 1.70E-05 5.88E+04
0.01 1.20E-05 8.33E+04
we can substitute for both yn and xn as follows:
y2 y1 8.33 104 4x104
4.81x106 5.0x106 dm3mol-1s-1 obtained graphically
x 2 x1 0.01 0.001
We can now rearrange the following formula to make T0 the subject:
1 1
k Q [Q]
T T0
1 1
k Q [Q]
T0 T
1 1
T0
1 1
T k Q [Q] 5
4.81x106 [0.01]
1.20x10
6
28.4x10 s 28.4s 28.6s obtained graphically
Please remember that units in both this and question 1 are very important. You will be
penalized for absence or incorrect units.
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